# Multi-Reference Parameter Estimation

ME'scope contains several different Multi-Reference Parameter Estimation (curve fitting) methods.
Each method uses the modal participation of each resonance in each reference to weight the data during curve fitting

## Multi-Reference Polynomial

This method uses a multi-reference version of the Rational Fraction Orthogonal Polynomial method, together with modal participations from a multiple reference Mode Indicator function

• The curve fitting model size in the Modes box on the Polynomial tab is used for estimating modal Frequency & Damping

## Stability Methods

These methods utilize a Stability diagram which doesn't require peak counting on a Mode Indicator function.

When the Multi-Reference Modal Analysis is enabled, Stability and Stable Groups tabs are added to the Frequency & Damping tab in a Data Block window.  The Stability tab contains curve fitting methods for estimating modal frequency & damping using a progression of curve fitting model sizes, from one mode up to the Max. Model Size listed on the tab.

### AF Polynomial (Alias Free Polynomial)

An extension of the Rational Fraction Orthogonal Polynomial method.
The term "alias free" refers to its characteristic of placing computational modes toward the edges of the curve fitting band, instead of aliasing them throughout the band.

### Complex Exponential

A time domain method that estimates poles by curve fitting Impulse Response Functions (IRFs).
During curve fitting, the Inverse FFT is applied to each FRF to obtain its corresponding IRF.

### Z Polynomial

An extension of the Rational Fraction Orthogonal Polynomial method.
Uses the Z transform to transform frequency to a unit circle, resulting in numerically stable solution equations.

## Methods Column

The curve fitting methods used to estimate the parameters of each mode are listed in the Frequency & Damping Method column, and the Residues Method column.  The following abbreviations are used for the curve fitting methods in the Multi-Reference Modal Analysis option,

• "AF Poly" Alias Free Polynomial

• "Comp Exp"  Complex Exponential

• "Z Poly"  Z Polynomial

• "M-Poly"  Multi-Reference Polynomial

• "M-AF Poly"  Multi-Reference AF Polynomial

• "M-Comp Exp"  Multi-Reference Complex Exponential

• "M-Z Poly"  Multi-Reference Z Polynomial